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In the accompanying diagram, three vertices of parallelogram ORST are O(0,0), R(b,d), and T(a,0). What are the coordinates of S?A. (a, b)B. (a+b, d)C. (a+b, b)D. (a, d)

In the accompanying diagram three vertices of parallelogram ORST are O00 Rbd and Ta0 What are the coordinates of SA a bB ab dC ab bD a d class=

Respuesta :

In a parallelogram, the opposite sides are parallel.

This means that RS is parallel to OT. So, the y value of S is the same as the y value of R, which is d, so y = d. Thus:

[tex]S=(x,y)=(x,d)[/tex]

Now, we need to find x.

Since the sides RO and ST are also parallel, the x distance from O to R is the same as the x distance from T to S.

The x distance from O to R is

[tex]b-0=b[/tex]

The x distance from T to S is

[tex]x-a[/tex]

Since these x distances are equal, then:

[tex]\begin{gathered} b=x-a \\ x=a+b \end{gathered}[/tex]

Then, the coordinates of S are:

[tex](a+b,d)[/tex]

Which corresponds to option B.

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